Explanation Given: a n = a n − 1 + n ( n + 1 ) 2 , a 1 = 1 … i Calculation: Now the characteristic equation of a n = a n − 1 + n ( n + 1 ) 2 , a 1 = 1 is x − 1 = 0 ⇒ g e n e r a l s o l u t i o n i s c ⋅ 1 n = c … i i The particular solution for n ( n + 1 ) 2 is of the form α n + β n 2 + γ n 3 . Substituting this in ( i ) we obtain α n + β n 2 + γ n 3 − ( α ( n − 1 ) + β ( n − 1 ) 2 + γ ( n − 1 ) 3 ) = n ( n + 1 ) 2 Putting values for n and simplif

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Chapter 8.2, Problem 37E

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Find the formula for the sum of the first n triangular numbers ∑1nk(k+1)2, by solving the recurrence equation: an=an−1+n(n+1)2, a1=1.

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Chapter 8.2, Problem 36E

Chapter 8.2, Problem 38E

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Chapter 8 Solutions

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

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Find the formula for the sum of the first n triangular numbers ∑ 1 n k ( k + 1 ) 2 , by solving the recurrence equation: a n = a n − 1 + n ( n + 1 ) 2 , a 1 = 1.

Solution Summary: The author calculates the formula for the sum of the first n triangular numbers by solving the recurrence equation.

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Find the formula for the sum of the first n triangular numbers ∑1nk(k+1)2, by solving the recurrence equation: an=an−1+n(n+1)2, a1=1.

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Chapter 8 Solutions